CN100571242C - Realize the method for Adaptive Modulation in a kind of ofdm system - Google Patents

Abstract

The invention discloses a kind of method that realizes Adaptive Modulation in ofdm system, (1) calculates the bit error rate P of each subcarrier _{M, c}(2) select all P of high modulation rank correspondence _{M, c}, calculate average error bit rate  _M(3) if  _MBe not more than target bit P _T, then this highest level modulation system is elected to be final modulation system; Otherwise to step (4); (4) if the P that calculates _{M, c}In, minimum P _{M, c}All surpassed P _T, then finish; Otherwise to step (5); (5), calculate its average error bit rate  at each subcarrier; (6) if  less than P _T, then increase peak value bit error rate , and to step (5), until the  that is calculated greater than P _TThe time, to step (7); (7) if  greater than P _T, then reduce , arrive step (5) once more, until the  that is calculated less than P _T, then become less than P first _T pairing that the group modulation system as final modulation system.Use the method for the invention, realized the Adaptive Modulation in system.

Description

Realize the method for Adaptive Modulation in a kind of ofdm system

Technical field

The present invention relates to a kind of OFDM (OFDM) wireless communication system, relate in particular to a kind of method that in ofdm system, realizes Adaptive Modulation.

Background technology

Along with development of wireless communication devices, the user has proposed higher requirement for large-capacity data emission and fast data transmission, therefore, need effectively utilize the wireless communication system resource, improves the performance and the efficient of wireless communication system.

Ofdm system is divided into several smooth narrowband subchannels with the broad-band channel with frequency selective fading of a reality, it is advantageous that can be according to the actual transmissions situation of each narrowband subchannels allocation of transmit power and information bit neatly, thereby effectively utilizes Radio Resource more.Adaptive Modulation a kind of distribution technique that comes to this, just system reasonably distributes the bit number that can transmit for each subcarrier under the prerequisite of knowing the channel condition information on all subcarriers.

The target of Adaptive Modulation of the present invention is for each subcarrier finds a kind of suitable modulation system, makes average error bit rate less than target bit, and to greatest extent near target bit.

Chinese patent CN200510000082 (a kind of bit and power distribution algorithm that is used for the ofdm system Adaptive Modulation) has announced a kind of self-adaptive modulation method, at first, according to the system applies environment, and the number of the self adaptation distribution processor that adopts of system, determine the grouping number N of subchannel _U, and the subchannel bunch subchannel number L that comprises in each grouping; Secondly, to all N _CThe individual subchannel that needs allocation bit and power according to they positions in frequency spectrum, is uniformly-spaced divided, and is divided into N _UIndividual grouping comprises the subchannel of similar number in each grouping; Then, in each grouping, carry out the distribution of bit and power respectively; In each grouping, carry out the branch timing of bit and power, at first according to the size of the amplitude of subchannel gains, to the subchannel in this grouping by from small to large or order from big to small sort; In each grouping, with the subchannel after the ordering, the mode by dividing continuously is divided into N then _SIndividual sub-cluster of channels (N _S=N _C/ (LN _U)), the subchannel number that comprises in each subchannel bunch is L; Next for each subchannel clusters into a sampling subchannel, the scheme that generates the sampling subchannel can be selected " least gain " scheme or " reciprocal average " scheme; Then the method for distributing by greediness on all sampling subchannels is carried out Bit Allocation in Discrete, and when carrying out Bit Allocation in Discrete by the method for greediness distribution, the bit number of actual required distribution is R _b/ (LN _U); After Bit Allocation in Discrete is intact,, duplicate, calculate the needed signal power of each subchannel at last respectively to each subchannel in the subchannel of correspondence bunch with the bit number that distributes on each sampling subchannel.

Said method has adopted greedy algorithm to come allocation bit, therefore is highly suitable for the ofdm system of fixed data rate.But in the ofdm system of reality, regular meeting changes during the residing channel circumstance of user, and in this case, it is unable to do what one wants very much to do that said method just seems.If continue to adopt fixed data rate, then can cause the huge waste of system resource.In addition, said method needed subchannel is divided into groups in allocation bit in the past, and the method for salary distribution of subcarrier is had strict restriction, had just increased the complexity of system like this in actual process relatively.

Thereby, in actual ofdm system, can not rely on the method for salary distribution of subcarrier fully and regulate modulation system according to the variation of channel adaptively, distribute suitable bit number, and then the maximization of realization data transfer rate, become problem demanding prompt solution in the industry.

Summary of the invention

The method that realizes Adaptive Modulation is provided to provide in a kind of ofdm system technical problem to be solved by this invention, with overcome prior art when carrying out the ofdm system Adaptive Modulation for the dependence of sub-carrier distribution manner and the defectives such as grouping of subchannel.

For solving the problems of the technologies described above, the invention provides a kind of method that in ofdm system, realizes Adaptive Modulation, comprise the steps:

(1) utilize the signal to noise ratio of each subcarrier respective channels, calculate each subcarrier the bit error rate under might modulation system;

(2) select all bit error rates of high modulation rank correspondence, calculate average error bit rate;

(3), then this highest level modulation system is elected to be final modulation system if described average error bit rate is not higher than target bit; Otherwise change step (4) over to;

(4) if in the bit error rate that calculates in the step (1), minimum bit error rate has all surpassed target bit, then all subcarriers is not distributed any bit, directly finishes; Otherwise change step (5) over to;

(5) in all bit error rates that step (1) calculates, at each subcarrier, select a bit error rate respectively, and, calculate average error bit rate according to the bit error rate combination of each subcarrier of selecting under the different modulating mode less than the peak value bit error rate;

(6) if the average error bit rate that calculates in the described step (5) less than target bit, then increases the peak value bit error rate, and change step (5) once more over to, during greater than target bit, change step (7) over to until the average error bit rate of being calculated;

(7) if the average error bit rate that calculates in the described step (5) greater than target bit, then reduce the peak value bit error rate, and then change step (5) over to, until the average error bit rate of being calculated less than target bit, then become first less than the average error bit rate of target bit pairing that the group modulation system will be selected as final modulation system.

Wherein, in the described step (5), the described step of selecting one less than the bit error rate of peak value bit error rate respectively if a subcarrier correspondence has a plurality of bit error rates less than the peak value bit error rate, is then selected wherein corresponding that the highest bit error rate of modulation levels.

Wherein, in the described step (5), described peak value bit error rate is passed through following steps and initial setting:

(51) utilize the signal to noise ratio of each subcarrier respective channels, calculate the bit error rate of all subcarriers under various possible modulation systems;

(52) at each subcarrier, under the condition of bit error rate, find out wherein maximum a bit error rate and corresponding modulation system thereof less than target bit, this bit error rate note is made α _{M, c}Simultaneously, under the condition of bit error rate, find out wherein minimum a bit error rate and corresponding modulation system thereof, this bit error rate note is made β greater than target bit _{M, c}, wherein, c represents sub-carrier indices number, m represents the m kind modulation system that each subcarrier can be supported;

(53) with all α _{M, c}In the β of a minimum identical modulation system of usefulness and subcarrier correspondence _{M, c}Replace;

(54) according to formula:

${\stackrel{\‾}{P}}_{\mathrm{\α}}=\frac{\underset{c=1}{\overset{C}{\mathrm{\Σ}}}{b}_{m,c}{\mathrm{\β}}_{m,c}}{\underset{c=1}{\overset{C}{\mathrm{\Σ}}}{b}_{m,c}}$ Formula (1)

Calculate average error bit rate P _α,

Wherein, b _{M, c}The bit number that transmits on the expression respective sub;

(55) the average error bit rate P of determining step (54) calculating _αWith target bit P _TMagnitude relationship, if average error bit rate, then changes step (53) over to less than target bit, the α that all are remaining _{M, c}In the β of a minimum identical modulation system of usefulness and subcarrier correspondence _{M, c}Replace; Otherwise change step (56) over to;

(56) at all α _{M, c}In, comprise the current α that is not replaced _{M, c}And the β that replaces _{M, c}, with size and maximum α _{M, c}α at an order of magnitude _{M, c}Concentrate in the set, the call number of its respective sub is included in this set, and utilizes formula:

$\mathrm{\ΔP}=\underset{c\∈S}{\mathrm{\Σ}}{b}_{m,c}(P_T-{\mathrm{\α}}_{m,c})$ Formula (2)

Calculate the difference of bit error rate;

(57) with β _{M, c}Arrange according to incremental order, begin stack from small to large, seek a maximum integer K, make:

$\mathrm{\ΔP}\≥\underset{k=0}{\overset{K}{\mathrm{\Σ}}}{b}_{m,c}({\mathrm{\β}}_{m,c}-P_T)$ Formula (3)

Under 0＜K＜C condition, β _{M, K}Corresponding bit error rate is exactly the initial spike bit error rate that is adopted; Wherein, C represents the available altogether number of sub carrier wave of described ofdm system.

The method that in ofdm system, realizes Adaptive Modulation of the present invention, under the certain prerequisite of mistake target bit rate, by adjusting the peak value bit error rate, make infinitely approaching between average error bit rate and the target bit, and then realized Adaptive Modulation process in ofdm system, satisfied the purpose that transmits information maximization.

Description of drawings

Fig. 1 is according to the described method flow schematic diagram of realizing Adaptive Modulation in ofdm system of the embodiment of the invention;

Fig. 2 is according to the described method flow schematic diagram of determining the initial spike bit error rate in realizing self-adaptive modulation method of the embodiment of the invention.

Embodiment

In OFDM (OFDM) system, Adaptive Modulation is exactly according to the channel variation on each subcarrier, selects suitable modulation system for each subcarrier, and the channel status performance index here can be signal to noise ratio (snr)s.In ofdm system,, make the information rate maximization of whole OFDM system if given transmitting power and bit error rate restrictive condition always can be the suitable modulation system of each subcarrier allocation according to channel condition information so adaptively.

The described core concept of the embodiment of the invention is exactly the signal to noise ratio according to subcarrier institute respective channels, calculates the bit error rate of subcarrier, and then the peak value bit error rate of this bit error rate and calculating is compared, to select suitable modulation system.

With reference to figure 1, be the described method flow diagram of in ofdm system, realizing Adaptive Modulation of present embodiment.Its process is as follows:

Step 101: utilize the signal to noise ratio of each subcarrier respective channels, calculate each subcarrier the bit error rate under might modulation system.Setting the available altogether number of sub carrier wave of ofdm system is C, and the modulation system that each subcarrier may be supported has the M kind.In the present embodiment, set, M=5 uses m=0 respectively, and 1,2,3,4 represent, representative does not distribute any bit, BPSK, QPSK, 16QAM, 64QAM successively.If subcarrier c (c=1,2 ..., adopted m kind modulation system on C), then the bit number that transmits on the respective sub is b _{M, c}, b _{M, c}The corresponding relation of value and modulation system is as follows:

m	0	1	2	3	4
						b m，c	0	1	2	4	6

If further suppose subcarrier c (c=1,2 ..., C) signal to noise ratio on is γ _c, then in theory, the bit error rate under the different modulating mode can be designated as P _{M, c}, at BPSK, corresponding P _{M, c}For

${\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="C2006100785840014H1.png,C2006100785840015H1.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,c}\left({\mathrm{\&gamma;}}_c\right)=Q\left(\sqrt{2{\mathrm{\&gamma;}}_c}\right)$ Formula (4)

For QPSK, 16QAM, 64QAM, its corresponding bit error rate is calculated according to formula (5)

$P_{m,c}\left({\mathrm{\&gamma;}}_c\right)=4(1-\frac{1}{\sqrt{M_m}})\&CenterDot;Q\left(\frac{3{\mathrm{\&gamma;}}_c}{M_m-1}\right)\&CenterDot;[1-(1-\frac{1}{\sqrt{M_m}})\&CenterDot;Q\left(\frac{3{\mathrm{\&gamma;}}_c}{M_m-1}\right)]$ Formula (5)

Plant in formula (5), m=2, in the time of 3,4, M _mValue is 4,16,64 respectively.In addition, Q (x) represents integral function

$Q\left(x\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}}{\&Integral;}_x^{+\&infin;}\exp \{-\frac{{\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="C2006100785840014H1.png"\; state="\{\{state\}\}">x</figure-callout>}}^2}{2}\}\mathrm{dx}$ Formula (6)

Like this, the bit error rate of all subcarriers under all modulation systems can be described with following table:

Step 102: in above table, select all bit error rates of high modulation rank correspondence, and calculate average error bit rate according to formula (7).The high modulation rank here is exactly 64QAM, and its corresponding bit error rate is exactly the P in the top form _{4, c}, then the bit number that transmits on the respective sub is b _{4, c}=6, so, average error bit rate is

${\stackrel{\&OverBar;}{P}}_4=\frac{\underset{c=1}{\overset{C}{\mathrm{\&Sigma;}}}{b}_{m,c}{\mathrm{\&beta;}}_{m,c}}{\underset{c=1}{\overset{C}{\mathrm{\&Sigma;}}}{b}_{m,c}}=\frac{\underset{c=1}{\overset{C}{\mathrm{\&Sigma;}}}6P_{4,c}}{\underset{c=1}{\overset{C}{\mathrm{\&Sigma;}}}6}=\frac{\underset{c=1}{\overset{C}{\mathrm{\&Sigma;}}}{P}_{4,c}}{C};$ Formula (7)

Step 103: judge average error bit rate P ₄Whether smaller or equal to target bit P _TIf,, change step 104 over to, if not, then change step 105 over to;

Step 104: the transmission of all subcarriers all is set to the 64QAM modulation system, finishes then;

Step 105: from all bit error rates that step 101 calculates, select a minimum P _{M, c}, whether judge this minimum bit error rate greater than target bit, if, change step 106 over to, if not, change step 107 over to;

Step 106:,, directly finish then so all subcarriers are not distributed any bit to such an extent as to can't transmit any bit information because this moment, channel status was too poor;

Step 107:, from all bit error rates that step 101 calculates, select the highest and bit error rate of modulation levels less than the peak value bit error rate at each subcarrier

Subcarrier and modulation mode combination, bit error rate that it is corresponding note is made ρ _{M, c}

Step 108: utilize the bit error rate ρ of each subcarrier under the different modulating mode that selects in the step 107 _{M, c}, utilize formula (8) to calculate the average error bit rate P of ofdm system;

$\stackrel{\&OverBar;}{P}=\frac{\underset{c=1}{\overset{C}{\mathrm{\&Sigma;}}}{b}_{m,c}{\mathrm{\&rho;}}_{m,c}}{\underset{c=1}{\overset{C}{\mathrm{\&Sigma;}}}{b}_{m,c}}$ Formula (8)

Step 109: judge that whether average error bit rate P is less than target bit P _TIf,, change step 111 over to, if not, change step 110 over to;

Step 110: with the peak value bit error rate

Remove a fixing value ξ, promptly $\hat{P}=\hat{P}-\mathrm{\&xi;},$ Change step 112 and step 113,114 then over to, carry out and step 107,108,109 similar operations, its purpose is to find the combination of one group of modulation system and subcarrier by adjusting the size of peak value bit error rate, makes average error bit rate just be lower than target bit P _T

Step 111: with the peak value bit error rate

Increase a fixing value ξ, promptly $\hat{P}=\hat{P}+\mathrm{\&xi;},$ Change step 107 then over to, continue the operation of execution in step 107,108,109, up to average error bit rate just above target bit P _T, changing step 110 then over to, the operation of execution in step 112,113,114 finds one group to make average error bit rate be about to surpass target bit P _TSubcarrier and modulation mode combination, this combination just is set to final transmission means;

Step 112:, from all bit error rates that step 101 calculates, select the highest and bit error rate of modulation levels less than the peak value bit error rate at each subcarrier Subcarrier and modulation mode combination, bit error rate that it is corresponding note is made ρ _{M, c}

Step 113: utilize the bit error rate ρ of each subcarrier under the different modulating mode that selects in the step 112 _{M, c}, utilize formula (8) to calculate the average error bit rate P of ofdm system;

Step 114: judge that whether average error bit rate P is less than target bit rate P _TIf,, then all subcarriers transmit with regard to the modulation system that is used to calculate this average error bit rate, finish then, if not, change step 112 over to.

Method as described in Figure 1, its convergence rate depends on the peak value bit error rate strongly

Selection, the purpose of choosing the initial spike bit error rate is exactly by adjusting the peak value bit error rate, realizing that average error bit rate and target bit are infinitely approaching.With reference to figure 2, for according to the described method flow schematic diagram of in realizing self-adaptive modulation method, determining the initial spike bit error rate of the embodiment of the invention.Detailed process is as follows:

Step 201: calculate the bit error rate P of all subcarriers under various modulation systems _{M, c}, also can directly utilize the result of calculation in the step 101 here;

Step 202: at each subcarrier, at corresponding bit error rate P _{M, c}Less than target bit P _TCondition under, find out wherein maximum bit error rate and corresponding modulation system thereof, this bit error rate note is made α _{M, c}

Step 203: at each subcarrier, at corresponding bit error rate P _{M, c}Greater than target bit P _TCondition under, find out wherein minimum bit error rate and corresponding modulation system thereof, this bit error rate note is made β _{M, c}

Step 204: from step 202, find out all α _{M, c}In, with the β of the identical modulation system of usefulness and the subcarrier correspondence of minimum _{M, c}Replace;

Step 205: calculate average error bit rate P according to formula (1) _α

Step 206: judge average error bit rate P _αWhether less than target bit P _TIf,, change step 204 over to, the α that all are remaining _{M, c}In the β of a minimum identical modulation system of usefulness and subcarrier correspondence _{M, c}Replace, if not, change step 207 over to;

Step 207: at all α _{M, c}(it comprises the α that the front was not replaced in the 3rd to the 5th step _{M, c}And the β that replaces _{M, c}, certainly, later β replaces _{M, c}Still be expressed as α _{M, c}) in, with size and maximum α _{M, c}α at an order of magnitude _{M, c}Concentrate in the set, the call number of its respective sub is included in the S set;

Step 208:, utilize all α in this set according to formula (2) _{M, c}Calculate the difference DELTA P of bit error rate, and store;

Step 209: with β _{M, c}Arrange according to incremental order, and begin stack from small to large, seek a maximum integer K, make

$\mathrm{\&Delta;P}\&GreaterEqual;\underset{k=0}{\overset{K}{\mathrm{\&Sigma;}}}{b}_{m,c}({\mathrm{\&beta;}}_{m,c}-P_T)$ Formula (3)

Under 0＜K＜C condition, β _{M, K}Corresponding bit error rate is exactly the initial spike bit error rate that is adopted

In the specific embodiment of the present invention, just for the example that 4 kinds of modulation systems are arranged, certainly, more than 4 kinds situation, its processing mode is also just the same, and just along with the increasing of mode kind, amount of calculation has increased.Embodiment provided by the invention is just for the method that realizes Adaptive Modulation in ofdm system that provides according to content of the present invention at large is provided; thereby all be exemplary execution mode; it can not be regarded as for restriction of the present invention; and every conspicuous modification within aim of the present invention is also due within protection scope of the present invention.

Claims (4)

1, realizes the method for Adaptive Modulation in a kind of ofdm system, it is characterized in that, comprise the steps:

(1) utilize the signal to noise ratio of each subcarrier respective channels, calculate each subcarrier the bit error rate under might modulation system;

(2) select all bit error rates of high modulation rank correspondence, calculate average error bit rate;

(3), then this highest level modulation system is elected to be final modulation system if described average error bit rate is not higher than target bit; Otherwise change step (4) over to;

(4) if in the bit error rate that calculates in the step (1), minimum bit error rate has all surpassed target bit, then all subcarriers is not distributed any bit, directly finishes; Otherwise change step (5) over to;

(5) in all bit error rates that step (1) calculates, at each subcarrier, select a bit error rate respectively, and, calculate average error bit rate according to the bit error rate combination of each subcarrier of selecting under the different modulating mode less than the peak value bit error rate;

(6) if the average error bit rate that calculates in the described step (5) less than target bit, then increases the peak value bit error rate, and change step (5) once more over to, during greater than target bit, change step (7) over to until the average error bit rate of being calculated;

(7) if the average error bit rate that calculates in the described step (5) greater than target bit, then reduce the peak value bit error rate, and then change step (5) over to, until the average error bit rate of being calculated less than target bit, then become first less than the average error bit rate of target bit pairing that the group modulation system will be selected as final modulation system.

2, the method for claim 1, it is characterized in that, in the described step (5), the described step of selecting one less than the bit error rate of peak value bit error rate respectively, if a subcarrier correspondence has a plurality of bit error rates less than the peak value bit error rate, then select wherein corresponding that the highest bit error rate of modulation levels.

3, the method for claim 1 is characterized in that, in the described step (1), each subcarrier of described calculating the step of the bit error rate under might modulation system, wherein, for the BPSK mode, corresponding bit error rate P _{M, c}Computing formula be:

$P_{1,c}\left({\mathrm{\&gamma;}}_c\right)=Q\left(\sqrt{2{\mathrm{\&gamma;}}_c}\right);$

For QPSK, 16QAM, 64QAM mode, its corresponding Bit Error Rate Computation formula is:

$P_{m,c}\left({\mathrm{\&gamma;}}_c\right)=4(1-\frac{1}{\sqrt{M_m}})\&CenterDot;Q\left(\frac{3{\mathrm{\&gamma;}}_c}{M_m-1}\right)\&CenterDot;[1-(1-\frac{1}{\sqrt{M_m}})\&CenterDot;Q\left(\frac{3{\mathrm{\&gamma;}}_c}{M_m-1}\right)]$

Wherein, γ _cFor subcarrier c (c=1,2 ..., the C) signal to noise ratio on, the modulation system that each subcarrier may be supported has the M kind, and m represents the m kind modulation system that each subcarrier can be supported, for QPSK, 16QAM, 64QAM, M _mValue is 4,16,64 respectively; Q (x) represents integral function:

$Q\left(x\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}}{\&Integral;}_x^{+\&infin;}\exp \{-\frac{x^2}{2}\}\mathrm{dx}.$

4, method as claimed in claim 3 is characterized in that, in the described step (5), described peak value bit error rate is passed through following steps and initial setting:

(51) utilize the signal to noise ratio of each subcarrier respective channels, calculate the bit error rate of all subcarriers under various possible modulation systems;

(52) at each subcarrier, under the condition of bit error rate, find out wherein maximum a bit error rate and corresponding modulation system thereof less than target bit, this bit error rate note is made α _{M, c}Simultaneously, under the condition of bit error rate, find out wherein minimum a bit error rate and corresponding modulation system thereof, this bit error rate note is made β greater than target bit _{M, c},

Wherein, c represents number of sub carrier wave, and m represents the m kind modulation system that each subcarrier can be supported;

(53) with all α _{M, c}In the β of a minimum identical modulation system of usefulness and subcarrier correspondence _{M, c}Replace;

(54) according to formula:

${\stackrel{\&OverBar;}{P}}_{\mathrm{\&alpha;}}=\frac{\underset{c=1}{\overset{C}{\mathrm{\&Sigma;}}}{b}_{m,c}{\mathrm{\&beta;}}_{m,c}}{\underset{c=1}{\overset{C}{\mathrm{\&Sigma;}}}{b}_{m,c}}$

Calculate average error bit rate P _α,

Wherein, b _{M, c}The bit number that transmits on the expression respective sub;

(55) the average error bit rate P of determining step (54) calculating _αWith target bit P _TMagnitude relationship, if average error bit rate, then changes step (53) over to less than target bit, the α that all are remaining _{M, c}In the β of a minimum identical modulation system of usefulness and subcarrier correspondence _{M, c}Replace; Otherwise change step (56) over to;

(56) at all α _{M, c}In, comprise the current α that is not replaced _{M, c}And the β that replaces _{M, c}, with size and maximum α _{M, c}α at an order of magnitude _{M, c}Concentrate in the set, the call number of its respective sub is included in this set, and utilizes formula:

$\mathrm{\&Delta;P}=\underset{c\&Element;S}{\mathrm{\&Sigma;}}{b}_{m,c}(P_T-{\mathrm{\&alpha;}}_{m,c})$

Calculate the difference of bit error rate;

(57) with β _{M, c}Arrange according to incremental order, begin stack from small to large, seek a maximum integer K, make:

$\mathrm{\&Delta;P}\&GreaterEqual;\underset{k=0}{\overset{K}{\mathrm{\&Sigma;}}}{b}_{m,c}({\mathrm{\&beta;}}_{m,c}-P_T)$

Under 0＜K＜C condition, β _{M, K}Corresponding bit error rate is exactly the initial spike bit error rate that is adopted; Wherein, C represents the available altogether number of sub carrier wave of described ofdm system.

Images